3D compact photonic circuits for realizing quantum state tomography of
qudits in any finite dimension
- URL: http://arxiv.org/abs/2002.04053v1
- Date: Mon, 10 Feb 2020 19:13:50 GMT
- Title: 3D compact photonic circuits for realizing quantum state tomography of
qudits in any finite dimension
- Authors: Wilder Cardoso, Davi Barros, Leonardo Neves, and Sebasti\~ao P\'adua
- Abstract summary: The POVM (Positive Operator-Valued Measure) chosen in this work ensures that, for odd dimensions, such process is minimal.
Based on the symmetry of the chosen POVM, the interferometer acting on the initial quantum system can be divided into a sequence of three different unitary operations.
- Score: 6.752249951921619
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we propose three-dimensional photonic circuit designs that
guarantee a considerable reduction in the complexity of circuits for the
purpose of performing quantum state tomography of N-dimensional path qudits.
The POVM (Positive Operator-Valued Measure) chosen in this work ensures that,
for odd dimensions, such process is minimal. Our proposal consists of
organizing the waveguides that form the circuit as a square array formed by N
vertical sectors composed of N waveguides each, arranged in the vertical
direction. Based on the symmetry of the chosen POVM, the interferometer acting
on the initial quantum system can be divided into a sequence of three different
unitary operations. These operations act independently on each vertical sector,
or layer, of the circuit, which simplifies their determination. We have thus
obtained circuits such that the number of beam splitters obeys a polynomial
function of degree 3 with the quantum system dimension, whereas in current
proposals this quantity grows with a polynomial function of degree 4. Besides
that, the optical depth is reduced from a quadratic to a linear function of the
quantum system dimension in our scheme. These results confirm the remarkable
reduction of the complexity of the photonic circuits in our proposal.
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